Problem: Solve for $x$ and $y$ using elimination. ${2x-5y = -20}$ ${-2x-3y = -44}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $2x$ and $-2x$ cancel out. $-8y = -64$ $\dfrac{-8y}{{-8}} = \dfrac{-64}{{-8}}$ ${y = 8}$ Now that you know ${y = 8}$ , plug it back into $\thinspace {2x-5y = -20}\thinspace$ to find $x$ ${2x - 5}{(8)}{= -20}$ $2x-40 = -20$ $2x-40{+40} = -20{+40}$ $2x = 20$ $\dfrac{2x}{{2}} = \dfrac{20}{{2}}$ ${x = 10}$ You can also plug ${y = 8}$ into $\thinspace {-2x-3y = -44}\thinspace$ and get the same answer for $x$ : ${-2x - 3}{(8)}{= -44}$ ${x = 10}$